First, defend the reasoning for your assigned solution using the wiki discussion page:
You may want to think about the following prompt: My solution is correct because I found the solution this way....
Tim G. --Solution 1
Tim T. --Solution 2
David ---Solution 1
Tom ------Solution 2
Liz --------Solution 1
Laura ----Solution 2
Max ------Solution 1
Sarah ----Solution 2
Second, respond to your partner's discussion post. Partners are grouped above.
You may want to think about the following prompts: You did a good job of explaining this... I don't understand this part of your reasoning....
Solution 1
So I figured that every triangle must be isawselleeys (you never taught us how to spell it!).
You can have a 1x1 triangle, 2x2 triangle, 3x3 triangle, 4x4 triangle, sq(2) triangle, 2sq(2) triangle.
It's easy to see the smallest triangle you can have, the 1x1 triangle. There's 32 of those.
Next, you have two of those triangles put together, which is a sq(2)xsq(2) triangle. I counted 24 of those.
You can't put 3 triangles together to make a triangle, but you can put 4! You get a 2x2 triangle. I counted 20 of those.
Next, you have the 2sq(2)x2sq(2), which is 8 triangles put together. I counted 8 of those.
Next, you have 3x3 triangle, which is 9 triangles put together. I counted 8 of those.
Finally, you have a 4x4 triangle, which is 16 triangles put together. I counted 4 of those.
So that's 32+24+20+8+8+4=96 triangles.
It's worth noting that I actually had 16 triangles for the sq(2)xsq(2) triangles but I didn't think that would be right. I thought that as you go from small triangles to bigger triangles to bigger triangles the number of triangles should decrease, so going from 32 to 16 to 20 didn't make sense. I recounted and got 24.
Solution 2
16 little triangles
4 big triangles, 4 other triangles
4 medium boxes – 16 medium triangles. 16 semi-medium triangles
1 big box in the middle – 4 triangles
16 + 4 + 16 + 16 + 4 + 4 = 64 triangles
The total area of the triangles is the total area of the figure, because all the triangles make up the figure.
I’m not sure what you mean by the total area of the triangles, because the 16 little triangles have the same area as the figure and so do the four big triangles. Am I supposed to subtract the area I already have accounted for?
You may want to think about the following prompt:
My solution is correct because I found the solution this way....
Tim G. --Solution 1
Tim T. --Solution 2
David ---Solution 1
Tom ------Solution 2
Liz --------Solution 1
Laura ----Solution 2
Max ------Solution 1
Sarah ----Solution 2
Second, respond to your partner's discussion post. Partners are grouped above.
You may want to think about the following prompts:
You did a good job of explaining this...
I don't understand this part of your reasoning....
Solution 1
So I figured that every triangle must be isawselleeys (you never taught us how to spell it!).
You can have a 1x1 triangle, 2x2 triangle, 3x3 triangle, 4x4 triangle, sq(2) triangle, 2sq(2) triangle.
It's easy to see the smallest triangle you can have, the 1x1 triangle. There's 32 of those.
Next, you have two of those triangles put together, which is a sq(2)xsq(2) triangle. I counted 24 of those.
You can't put 3 triangles together to make a triangle, but you can put 4! You get a 2x2 triangle. I counted 20 of those.
Next, you have the 2sq(2)x2sq(2), which is 8 triangles put together. I counted 8 of those.
Next, you have 3x3 triangle, which is 9 triangles put together. I counted 8 of those.
Finally, you have a 4x4 triangle, which is 16 triangles put together. I counted 4 of those.
So that's 32+24+20+8+8+4=96 triangles.
It's worth noting that I actually had 16 triangles for the sq(2)xsq(2) triangles but I didn't think that would be right. I thought that as you go from small triangles to bigger triangles to bigger triangles the number of triangles should decrease, so going from 32 to 16 to 20 didn't make sense. I recounted and got 24.
Solution 2
16 little triangles
4 big triangles, 4 other triangles
4 medium boxes – 16 medium triangles. 16 semi-medium triangles
1 big box in the middle – 4 triangles
16 + 4 + 16 + 16 + 4 + 4 = 64 triangles
The total area of the triangles is the total area of the figure, because all the triangles make up the figure.
I’m not sure what you mean by the total area of the triangles, because the 16 little triangles have the same area as the figure and so do the four big triangles. Am I supposed to subtract the area I already have accounted for?